Question

A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the same number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time per week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week.

A. No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100B
B. No, because the bike order does not meet the restrictions of 4c ≤ 120 and 6c + 4a ≤ 100
C. Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
D. Yes, because the bike order meets the restrictions of 4c ≤ 120 and 6c + 4a ≤ 100

Answer 1

The company cannot build 20 child bikes and 6 adult bikes within a week because the building time meets the constraints, but the testing time exceeds the limit set by the inequalities.Therefore, the answer is: B. No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100.

Step-by-step explanation:

The question involves determining whether a bicycle manufacturing company can build 20 child bikes and 6 adult bikes within a given timeframe, given the constraints on building and testing hours.

The variables c and a represent child bikes and adult bikes, respectively.

Each child bike requires 4 hours to build and 4 hours to test, while each adult bike requires 6 hours to build and 4 hours to test.

The company has up to 120 hours of building time and 100 hours of testing time per week.

To find out whether the company can meet the demand for 20 child bikes and 6 adult bikes, we need to plug the values into the inequalities provided:

Building Time Inequality: 4c + 6a ≤ 120

Testing Time Inequality: 4c + 4a ≤ 100

Let's apply these inequalities to the proposed situation:

Building Time: 4(20) + 6(6) = 80 + 36 = 116 ≤ 120

Testing Time: 4(20) + 4(6) = 80 + 24 = 104 ≤ 100

The building time of 116 hours does not exceed the available 120 hours, but the testing time of 104 hours exceeds the available 100 hours.

Therefore, the answer is: B. No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100.